A Soldier Frozen In Time

I am clearly not a psychiatrist but I have had many experiences with characters in books that are mentally ill. The reader does not realise immediately that the character is suffering from a mental disorder and also loses sense of what reality is in the book. In slaughterhouse five we ca observe this with Billy Pilgrim. Pilgrim may be suffering from a severe mental disorder called Post-traumatic Stress Disorder, which results from psychological trauma.

Billy has witnessed extreme pain and suffering because of the war. In fact, as is mentioned in the book, Billy was present in one of Europe's greatest massacres, the bombing of Dresden. Imagine the impact that this may have had on Billy. Seeing all those people killed, families slowly disintegrating, and simply all the horrible emotions that came with war. This must have scarred Billy for life, causing him Post Traumatic Stress Disorder. This would explain why Billy has no sense of reality and can travel back in time. We all know that sure one day this may be possible, but that for now travelling in time is not an option. One of the symptoms of PTSD is a loss of interest in activities and life in general, which is actually occurring to Billy in the book. Billy and Rosewater have both lost interest in life as is observed in the following phrases: "Rosewater was twice as smart as Billy, but he and Billy were dealing with similar crises in similar ways. They had both found life meaningless, partly because of what they had seen in war." (p. 101)  

Besides this, Vonnegut also mentions repeatedly that Billy is or was in a mental institution as a patient. We don't know if Billy is in the mental institution in the present or if this occurred early in his life. Could our main character, Billy Pilgrim, be in a mental hospital because of PTSD?